The discussion centers on proving the vector property for R(t) = <f(t), g(t), h(t)>, specifically D_t[R(t) X R'(t)] = R(t) X R"(t). Participants clarify that the cross product is denoted by "X" and confirm that the derivative D_t refers to the derivative with respect to t. They emphasize the importance of applying the product rule for vector products, which leads to the realization that the initial equation was miscopied from a textbook. This correction helps participants understand the relationship between the derivatives involved. The conversation concludes with a sense of clarity regarding the proof process.